Here is the sentence:
I lost my wife, she went shopping & hasn’t come back yet.
Using present perfect here is right or wrong? And I remember that (or I remember wrong) after ‘and’, verb must be following with the tense before ‘and’ (in this case is Past Simple tense) – it’s right or wrong? Thanks so much!
The sentence is (mostly) fine. There is no rule that says that all the verbs in a sentence have to be in the same tense. Sometimes the sentence makes more sense and reads better if the tenses match, but sometimes, like in your example, that wouldn’t make any sense.
She went shopping – this happened entirely in the past, so the simple past is appropriate.
(She) hasn’t come back yet – this began in the past and continues until the present, so the present perfect is appropriate.
When you think about it, there are lots of cases in which you would use different tenses in one sentence, e.g. “Yesterday I lost my glasses and tomorrow I will buy new ones” or “I had never seen an elephant until I went to the zoo, but I still haven’t seen a tiger.”
(The one correction I would make to the sentence is that it’s using what’s called a comma splice. “I lost my wife” is a completely separate main clause from “She went shopping and hasn’t come back yet”, and you can’t join two independent clauses with a comma. You need to separate them into two sentences with a period, or connect them with a semicolon or a conjunction like “and” or “because”.)